10 questions · Form 4 Mathematics Bab 2: Number Bases
Which digit has a place value of 5³ in the number 2413₅?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Which digit has a place value of 5³ in the number 2413₅?
Answer: A
From right to left, place values are 5⁰ (3), 5¹ (1), 5² (4), 5³ (2). The digit is 2.
2. Convert 234₅ to Base 8.
Answer: A
First convert 234₅ to Base 10: (2×25) + (3×5) + 4 = 50 + 15 + 4 = 69₁₀. Then 69 to Base 8: 69 ÷ 8 = 8 rem 5; 8 ÷ 8 = 1 rem 0; 1 ÷ 8 = 0 rem 1. Yields 105₈. Wait, let's recalculate: 69 ÷ 8 = 8 rem 5; 8 ÷ 8 = 1 rem 0; 1 ÷ 8 = 0 rem 1 -> 105₈. Let's adjust correct option: Option A = 105₈.
3. Given 101₂ + x₂ = 1000₂, find the value of x in Base 2.
Answer: A
x₂ = 1000₂ - 101₂ = 8₁₀ - 5₁₀ = 3₁₀. Converting 3₁₀ to binary gives 11₂.
4. Calculate the digit value of 3 in the number 5312₈.
Answer: B
The place value of digit 3 is 8². Digit value = 3 × 8² = 3 × 64 = 192.
5. If x₈ = 101110₂, find the value of x.
Answer: A
Group binary in threes from right: (101)(110)₂ = 56₈. Thus x = 56.
6. A computer uses Base 16 (hexadecimal) where digits go from 0-9 and A-F. If A=10, B=11, C=12, D=13, E=14, F=15, convert 2B₁₆ to Base 10.
Answer: A
2B₁₆ = (2 × 16¹) + (11 × 16⁰) = 32 + 11 = 43₁₀.
7. Express 1011001₂ directly as a number in Base 8.
Answer: A
Group in threes from right: (001)(011)(001) -> 001₂ = 1, 011₂ = 3, 001₂ = 1. Combining yields 131₈.
8. Convert 405₉ into Base 10.
Answer: A
405₉ = (4 × 9²) + (0 × 9¹) + (5 × 9⁰) = (4 × 81) + 0 + 5 = 324 + 5 = 329₁₀.
9. Which of the following numbers is NOT a valid number in Base 5?
Answer: C
A Base 5 number can only contain digits from 0 to 4. Option C contains the digit '5', making it invalid.
10. Find the sum of 432₅ and 234₅ in Base 5.
Answer: A
2+4 = 6 = 11₅ (write 1, carry 1). 1+3+3 = 7 = 12₅ (write 2, carry 1). 1+4+2 = 7 = 12₅. Answer = 1221₅.